Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.5% → 94.5%

Time: 7.0s

Alternatives: 10

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.6%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

2. Final simplification 94.6%

   \[\leadsto x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

Alternative 2: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-64}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+210}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.6e+142)
   (* x (/ t z))
   (if (<= t 1.9e-64)
     (/ (* x y) z)
     (if (<= t 4.4e+210) (* y (/ x z)) (/ x (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.6e+142) {
		tmp = x * (t / z);
	} else if (t <= 1.9e-64) {
		tmp = (x * y) / z;
	} else if (t <= 4.4e+210) {
		tmp = y * (x / z);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.6d+142)) then
        tmp = x * (t / z)
    else if (t <= 1.9d-64) then
        tmp = (x * y) / z
    else if (t <= 4.4d+210) then
        tmp = y * (x / z)
    else
        tmp = x / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.6e+142) {
		tmp = x * (t / z);
	} else if (t <= 1.9e-64) {
		tmp = (x * y) / z;
	} else if (t <= 4.4e+210) {
		tmp = y * (x / z);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.6e+142:
		tmp = x * (t / z)
	elif t <= 1.9e-64:
		tmp = (x * y) / z
	elif t <= 4.4e+210:
		tmp = y * (x / z)
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.6e+142)
		tmp = Float64(x * Float64(t / z));
	elseif (t <= 1.9e-64)
		tmp = Float64(Float64(x * y) / z);
	elseif (t <= 4.4e+210)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.6e+142)
		tmp = x * (t / z);
	elseif (t <= 1.9e-64)
		tmp = (x * y) / z;
	elseif (t <= 4.4e+210)
		tmp = y * (x / z);
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.6e+142], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-64], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 4.4e+210], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.6e142

   1. Initial program 99.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 69.3%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. sub-neg 69.3%

         \[\leadsto \frac{\color{blue}{\left(y + \left(--1 \cdot t\right)\right)} \cdot x}{z} \]

      2. remove-double-neg 69.3%

         \[\leadsto \frac{\left(\color{blue}{\left(-\left(-y\right)\right)} + \left(--1 \cdot t\right)\right) \cdot x}{z} \]

      3. neg-mul-1 69.3%

         \[\leadsto \frac{\left(\left(-\left(-y\right)\right) + \left(-\color{blue}{\left(-t\right)}\right)\right) \cdot x}{z} \]

      4. distribute-neg-in 69.3%

         \[\leadsto \frac{\color{blue}{\left(-\left(\left(-y\right) + \left(-t\right)\right)\right)} \cdot x}{z} \]

      5. neg-mul-1 69.3%

         \[\leadsto \frac{\left(-\left(\color{blue}{-1 \cdot y} + \left(-t\right)\right)\right) \cdot x}{z} \]

      6. sub-neg 69.3%

         \[\leadsto \frac{\left(-\color{blue}{\left(-1 \cdot y - t\right)}\right) \cdot x}{z} \]

      7. distribute-lft-neg-in 69.3%

         \[\leadsto \frac{\color{blue}{-\left(-1 \cdot y - t\right) \cdot x}}{z} \]

      8. distribute-neg-frac 69.3%

         \[\leadsto \color{blue}{-\frac{\left(-1 \cdot y - t\right) \cdot x}{z}} \]

      9. associate-/l* 71.9%

         \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{\frac{z}{x}}} \]

      10. associate-/r/ 83.3%

          \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{z} \cdot x} \]

      11. distribute-lft-neg-in 83.3%

          \[\leadsto \color{blue}{\left(-\frac{-1 \cdot y - t}{z}\right) \cdot x} \]

   4. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{y + t}{z} \cdot x} \]

   5. Taylor expanded in y around 0 62.1%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-/l* 64.6%

         \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]

      2. associate-/r/ 73.8%

         \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   7. Simplified 73.8%

      \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   if -5.6e142 < t < 1.9000000000000001e-64

   1. Initial program 92.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in y around inf 84.4%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]

   if 1.9000000000000001e-64 < t < 4.39999999999999974e210

   1. Initial program 94.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 61.9%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 61.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 69.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 69.5%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 69.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around inf 55.1%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 67.7%

         \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   7. Simplified 67.7%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   if 4.39999999999999974e210 < t

   1. Initial program 99.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 59.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 69.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 69.0%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around 0 58.5%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{t}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-64}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+210}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 3: 88.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -27 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -27.0) (not (<= z 1.0)))
   (* (+ y t) (/ x z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -27.0) || !(z <= 1.0)) {
		tmp = (y + t) * (x / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-27.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y + t) * (x / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -27.0) || !(z <= 1.0)) {
		tmp = (y + t) * (x / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -27.0) or not (z <= 1.0):
		tmp = (y + t) * (x / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -27.0) || !(z <= 1.0))
		tmp = Float64(Float64(y + t) * Float64(x / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -27.0) || ~((z <= 1.0)))
		tmp = (y + t) * (x / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -27.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y + t), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -27 or 1 < z

   1. Initial program 95.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Step-by-step derivation

      1. frac-2neg 95.5%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-y}{-z}} - \frac{t}{1 - z}\right) \]

      2. div-inv 95.4%

         \[\leadsto x \cdot \left(\color{blue}{\left(-y\right) \cdot \frac{1}{-z}} - \frac{t}{1 - z}\right) \]

      3. fma-neg 95.4%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-y, \frac{1}{-z}, -\frac{t}{1 - z}\right)} \]

      4. distribute-neg-frac 95.4%

         \[\leadsto x \cdot \mathsf{fma}\left(-y, \frac{1}{-z}, \color{blue}{\frac{-t}{1 - z}}\right) \]

   3. Applied egg-rr 95.4%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-y, \frac{1}{-z}, \frac{-t}{1 - z}\right)} \]
   4. Step-by-step derivation

      1. distribute-frac-neg 95.4%

         \[\leadsto x \cdot \mathsf{fma}\left(-y, \frac{1}{-z}, \color{blue}{-\frac{t}{1 - z}}\right) \]

      2. fma-neg 95.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot \frac{1}{-z} - \frac{t}{1 - z}\right)} \]

      3. neg-mul-1 95.4%

         \[\leadsto x \cdot \left(\left(-y\right) \cdot \frac{1}{\color{blue}{-1 \cdot z}} - \frac{t}{1 - z}\right) \]

      4. associate-/r* 95.4%

         \[\leadsto x \cdot \left(\left(-y\right) \cdot \color{blue}{\frac{\frac{1}{-1}}{z}} - \frac{t}{1 - z}\right) \]

      5. metadata-eval 95.4%

         \[\leadsto x \cdot \left(\left(-y\right) \cdot \frac{\color{blue}{-1}}{z} - \frac{t}{1 - z}\right) \]

   5. Simplified 95.4%

      \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot \frac{-1}{z} - \frac{t}{1 - z}\right)} \]

   6. Taylor expanded in z around inf 87.5%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 86.2%

         \[\leadsto \color{blue}{\frac{y - -1 \cdot t}{\frac{z}{x}}} \]

      2. cancel-sign-sub-inv 86.2%

         \[\leadsto \frac{\color{blue}{y + \left(--1\right) \cdot t}}{\frac{z}{x}} \]

      3. metadata-eval 86.2%

         \[\leadsto \frac{y + \color{blue}{1} \cdot t}{\frac{z}{x}} \]

      4. *-lft-identity 86.2%

         \[\leadsto \frac{y + \color{blue}{t}}{\frac{z}{x}} \]

      5. associate-/l* 87.5%

         \[\leadsto \color{blue}{\frac{\left(y + t\right) \cdot x}{z}} \]

      6. associate-*r/ 87.2%

         \[\leadsto \color{blue}{\left(y + t\right) \cdot \frac{x}{z}} \]

   8. Simplified 87.2%

      \[\leadsto \color{blue}{\left(y + t\right) \cdot \frac{x}{z}} \]

   if -27 < z < 1

   1. Initial program 93.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around 0 94.0%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*l/ 90.4%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} + -1 \cdot \left(t \cdot x\right) \]

      2. associate-*r* 90.4%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

      3. neg-mul-1 90.4%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-t\right)} \cdot x \]

      4. distribute-rgt-out 93.6%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} + \left(-t\right)\right)} \]

      5. unsub-neg 93.6%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} - t\right)} \]

   4. Simplified 93.6%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -27 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 4: 93.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -27 \lor \neg \left(z \leq 2.4 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -27.0) (not (<= z 2.4e-12)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -27.0) || !(z <= 2.4e-12)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-27.0d0)) .or. (.not. (z <= 2.4d-12))) then
        tmp = x * ((y + t) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -27.0) || !(z <= 2.4e-12)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -27.0) or not (z <= 2.4e-12):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -27.0) || !(z <= 2.4e-12))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -27.0) || ~((z <= 2.4e-12)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -27.0], N[Not[LessEqual[z, 2.4e-12]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -27 or 2.39999999999999987e-12 < z

   1. Initial program 95.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 87.6%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. sub-neg 87.6%

         \[\leadsto \frac{\color{blue}{\left(y + \left(--1 \cdot t\right)\right)} \cdot x}{z} \]

      2. remove-double-neg 87.6%

         \[\leadsto \frac{\left(\color{blue}{\left(-\left(-y\right)\right)} + \left(--1 \cdot t\right)\right) \cdot x}{z} \]

      3. neg-mul-1 87.6%

         \[\leadsto \frac{\left(\left(-\left(-y\right)\right) + \left(-\color{blue}{\left(-t\right)}\right)\right) \cdot x}{z} \]

      4. distribute-neg-in 87.6%

         \[\leadsto \frac{\color{blue}{\left(-\left(\left(-y\right) + \left(-t\right)\right)\right)} \cdot x}{z} \]

      5. neg-mul-1 87.6%

         \[\leadsto \frac{\left(-\left(\color{blue}{-1 \cdot y} + \left(-t\right)\right)\right) \cdot x}{z} \]

      6. sub-neg 87.6%

         \[\leadsto \frac{\left(-\color{blue}{\left(-1 \cdot y - t\right)}\right) \cdot x}{z} \]

      7. distribute-lft-neg-in 87.6%

         \[\leadsto \frac{\color{blue}{-\left(-1 \cdot y - t\right) \cdot x}}{z} \]

      8. distribute-neg-frac 87.6%

         \[\leadsto \color{blue}{-\frac{\left(-1 \cdot y - t\right) \cdot x}{z}} \]

      9. associate-/l* 86.3%

         \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{\frac{z}{x}}} \]

      10. associate-/r/ 95.3%

          \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{z} \cdot x} \]

      11. distribute-lft-neg-in 95.3%

          \[\leadsto \color{blue}{\left(-\frac{-1 \cdot y - t}{z}\right) \cdot x} \]

   4. Simplified 95.3%

      \[\leadsto \color{blue}{\frac{y + t}{z} \cdot x} \]

   if -27 < z < 2.39999999999999987e-12

   1. Initial program 93.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around 0 93.9%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*l/ 90.3%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} + -1 \cdot \left(t \cdot x\right) \]

      2. associate-*r* 90.3%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

      3. neg-mul-1 90.3%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-t\right)} \cdot x \]

      4. distribute-rgt-out 93.6%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} + \left(-t\right)\right)} \]

      5. unsub-neg 93.6%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} - t\right)} \]

   4. Simplified 93.6%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -27 \lor \neg \left(z \leq 2.4 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 5: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.4e+142)
   (* x (/ t z))
   (if (<= t 4.4e-87) (/ (* x y) z) (* x (- (/ y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.4e+142) {
		tmp = x * (t / z);
	} else if (t <= 4.4e-87) {
		tmp = (x * y) / z;
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.4d+142)) then
        tmp = x * (t / z)
    else if (t <= 4.4d-87) then
        tmp = (x * y) / z
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.4e+142) {
		tmp = x * (t / z);
	} else if (t <= 4.4e-87) {
		tmp = (x * y) / z;
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.4e+142:
		tmp = x * (t / z)
	elif t <= 4.4e-87:
		tmp = (x * y) / z
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.4e+142)
		tmp = Float64(x * Float64(t / z));
	elseif (t <= 4.4e-87)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.4e+142)
		tmp = x * (t / z);
	elseif (t <= 4.4e-87)
		tmp = (x * y) / z;
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.4e+142], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-87], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.39999999999999974e142

   1. Initial program 99.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 69.3%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. sub-neg 69.3%

         \[\leadsto \frac{\color{blue}{\left(y + \left(--1 \cdot t\right)\right)} \cdot x}{z} \]

      2. remove-double-neg 69.3%

         \[\leadsto \frac{\left(\color{blue}{\left(-\left(-y\right)\right)} + \left(--1 \cdot t\right)\right) \cdot x}{z} \]

      3. neg-mul-1 69.3%

         \[\leadsto \frac{\left(\left(-\left(-y\right)\right) + \left(-\color{blue}{\left(-t\right)}\right)\right) \cdot x}{z} \]

      4. distribute-neg-in 69.3%

         \[\leadsto \frac{\color{blue}{\left(-\left(\left(-y\right) + \left(-t\right)\right)\right)} \cdot x}{z} \]

      5. neg-mul-1 69.3%

         \[\leadsto \frac{\left(-\left(\color{blue}{-1 \cdot y} + \left(-t\right)\right)\right) \cdot x}{z} \]

      6. sub-neg 69.3%

         \[\leadsto \frac{\left(-\color{blue}{\left(-1 \cdot y - t\right)}\right) \cdot x}{z} \]

      7. distribute-lft-neg-in 69.3%

         \[\leadsto \frac{\color{blue}{-\left(-1 \cdot y - t\right) \cdot x}}{z} \]

      8. distribute-neg-frac 69.3%

         \[\leadsto \color{blue}{-\frac{\left(-1 \cdot y - t\right) \cdot x}{z}} \]

      9. associate-/l* 71.9%

         \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{\frac{z}{x}}} \]

      10. associate-/r/ 83.3%

          \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{z} \cdot x} \]

      11. distribute-lft-neg-in 83.3%

          \[\leadsto \color{blue}{\left(-\frac{-1 \cdot y - t}{z}\right) \cdot x} \]

   4. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{y + t}{z} \cdot x} \]

   5. Taylor expanded in y around 0 62.1%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-/l* 64.6%

         \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]

      2. associate-/r/ 73.8%

         \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   7. Simplified 73.8%

      \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   if -4.39999999999999974e142 < t < 4.39999999999999976e-87

   1. Initial program 92.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in y around inf 85.7%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]

   if 4.39999999999999976e-87 < t

   1. Initial program 96.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around 0 61.5%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*l/ 61.3%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} + -1 \cdot \left(t \cdot x\right) \]

      2. associate-*r* 61.3%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-1 \cdot t\right) \cdot x} \]

      3. neg-mul-1 61.3%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\left(-t\right)} \cdot x \]

      4. distribute-rgt-out 64.0%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} + \left(-t\right)\right)} \]

      5. unsub-neg 64.0%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} - t\right)} \]

   4. Simplified 64.0%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 6: 66.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+142} \lor \neg \left(t \leq 4.4 \cdot 10^{+210}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.2e+142) (not (<= t 4.4e+210))) (* x (/ t z)) (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e+142) || !(t <= 4.4e+210)) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5.2d+142)) .or. (.not. (t <= 4.4d+210))) then
        tmp = x * (t / z)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e+142) || !(t <= 4.4e+210)) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.2e+142) or not (t <= 4.4e+210):
		tmp = x * (t / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.2e+142) || !(t <= 4.4e+210))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.2e+142) || ~((t <= 4.4e+210)))
		tmp = x * (t / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.2e+142], N[Not[LessEqual[t, 4.4e+210]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.20000000000000043e142 or 4.39999999999999974e210 < t

   1. Initial program 99.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 66.1%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. sub-neg 66.1%

         \[\leadsto \frac{\color{blue}{\left(y + \left(--1 \cdot t\right)\right)} \cdot x}{z} \]

      2. remove-double-neg 66.1%

         \[\leadsto \frac{\left(\color{blue}{\left(-\left(-y\right)\right)} + \left(--1 \cdot t\right)\right) \cdot x}{z} \]

      3. neg-mul-1 66.1%

         \[\leadsto \frac{\left(\left(-\left(-y\right)\right) + \left(-\color{blue}{\left(-t\right)}\right)\right) \cdot x}{z} \]

      4. distribute-neg-in 66.1%

         \[\leadsto \frac{\color{blue}{\left(-\left(\left(-y\right) + \left(-t\right)\right)\right)} \cdot x}{z} \]

      5. neg-mul-1 66.1%

         \[\leadsto \frac{\left(-\left(\color{blue}{-1 \cdot y} + \left(-t\right)\right)\right) \cdot x}{z} \]

      6. sub-neg 66.1%

         \[\leadsto \frac{\left(-\color{blue}{\left(-1 \cdot y - t\right)}\right) \cdot x}{z} \]

      7. distribute-lft-neg-in 66.1%

         \[\leadsto \frac{\color{blue}{-\left(-1 \cdot y - t\right) \cdot x}}{z} \]

      8. distribute-neg-frac 66.1%

         \[\leadsto \color{blue}{-\frac{\left(-1 \cdot y - t\right) \cdot x}{z}} \]

      9. associate-/l* 69.3%

         \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{\frac{z}{x}}} \]

      10. associate-/r/ 78.8%

          \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{z} \cdot x} \]

      11. distribute-lft-neg-in 78.8%

          \[\leadsto \color{blue}{\left(-\frac{-1 \cdot y - t}{z}\right) \cdot x} \]

   4. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{y + t}{z} \cdot x} \]

   5. Taylor expanded in y around 0 57.8%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-/l* 61.1%

         \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]

      2. associate-/r/ 68.9%

         \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   if -5.20000000000000043e142 < t < 4.39999999999999974e210

   1. Initial program 93.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 80.6%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 80.6%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 79.1%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 79.1%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 79.1%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around inf 77.1%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 75.6%

         \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   7. Simplified 75.6%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+142} \lor \neg \left(t \leq 4.4 \cdot 10^{+210}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 7: 67.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+142} \lor \neg \left(t \leq 4.4 \cdot 10^{+210}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.9e+142) (not (<= t 4.4e+210))) (* x (/ t z)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.9e+142) || !(t <= 4.4e+210)) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.9d+142)) .or. (.not. (t <= 4.4d+210))) then
        tmp = x * (t / z)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.9e+142) || !(t <= 4.4e+210)) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.9e+142) or not (t <= 4.4e+210):
		tmp = x * (t / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.9e+142) || !(t <= 4.4e+210))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.9e+142) || ~((t <= 4.4e+210)))
		tmp = x * (t / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.9e+142], N[Not[LessEqual[t, 4.4e+210]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9e142 or 4.39999999999999974e210 < t

   1. Initial program 99.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 66.1%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. sub-neg 66.1%

         \[\leadsto \frac{\color{blue}{\left(y + \left(--1 \cdot t\right)\right)} \cdot x}{z} \]

      2. remove-double-neg 66.1%

         \[\leadsto \frac{\left(\color{blue}{\left(-\left(-y\right)\right)} + \left(--1 \cdot t\right)\right) \cdot x}{z} \]

      3. neg-mul-1 66.1%

         \[\leadsto \frac{\left(\left(-\left(-y\right)\right) + \left(-\color{blue}{\left(-t\right)}\right)\right) \cdot x}{z} \]

      4. distribute-neg-in 66.1%

         \[\leadsto \frac{\color{blue}{\left(-\left(\left(-y\right) + \left(-t\right)\right)\right)} \cdot x}{z} \]

      5. neg-mul-1 66.1%

         \[\leadsto \frac{\left(-\left(\color{blue}{-1 \cdot y} + \left(-t\right)\right)\right) \cdot x}{z} \]

      6. sub-neg 66.1%

         \[\leadsto \frac{\left(-\color{blue}{\left(-1 \cdot y - t\right)}\right) \cdot x}{z} \]

      7. distribute-lft-neg-in 66.1%

         \[\leadsto \frac{\color{blue}{-\left(-1 \cdot y - t\right) \cdot x}}{z} \]

      8. distribute-neg-frac 66.1%

         \[\leadsto \color{blue}{-\frac{\left(-1 \cdot y - t\right) \cdot x}{z}} \]

      9. associate-/l* 69.3%

         \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{\frac{z}{x}}} \]

      10. associate-/r/ 78.8%

          \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{z} \cdot x} \]

      11. distribute-lft-neg-in 78.8%

          \[\leadsto \color{blue}{\left(-\frac{-1 \cdot y - t}{z}\right) \cdot x} \]

   4. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{y + t}{z} \cdot x} \]

   5. Taylor expanded in y around 0 57.8%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-/l* 61.1%

         \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]

      2. associate-/r/ 68.9%

         \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   if -3.9e142 < t < 4.39999999999999974e210

   1. Initial program 93.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in y around inf 77.1%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   3. Step-by-step derivation

      1. associate-*l/ 76.4%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]

   4. Simplified 76.4%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+142} \lor \neg \left(t \leq 4.4 \cdot 10^{+210}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 8: 67.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+211}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.5e+142)
   (* x (/ t z))
   (if (<= t 9.5e+211) (* x (/ y z)) (/ x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.5e+142) {
		tmp = x * (t / z);
	} else if (t <= 9.5e+211) {
		tmp = x * (y / z);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.5d+142)) then
        tmp = x * (t / z)
    else if (t <= 9.5d+211) then
        tmp = x * (y / z)
    else
        tmp = x / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.5e+142) {
		tmp = x * (t / z);
	} else if (t <= 9.5e+211) {
		tmp = x * (y / z);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.5e+142:
		tmp = x * (t / z)
	elif t <= 9.5e+211:
		tmp = x * (y / z)
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.5e+142)
		tmp = Float64(x * Float64(t / z));
	elseif (t <= 9.5e+211)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.5e+142)
		tmp = x * (t / z);
	elseif (t <= 9.5e+211)
		tmp = x * (y / z);
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.5e+142], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+211], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.50000000000000035e142

   1. Initial program 99.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 69.3%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. sub-neg 69.3%

         \[\leadsto \frac{\color{blue}{\left(y + \left(--1 \cdot t\right)\right)} \cdot x}{z} \]

      2. remove-double-neg 69.3%

         \[\leadsto \frac{\left(\color{blue}{\left(-\left(-y\right)\right)} + \left(--1 \cdot t\right)\right) \cdot x}{z} \]

      3. neg-mul-1 69.3%

         \[\leadsto \frac{\left(\left(-\left(-y\right)\right) + \left(-\color{blue}{\left(-t\right)}\right)\right) \cdot x}{z} \]

      4. distribute-neg-in 69.3%

         \[\leadsto \frac{\color{blue}{\left(-\left(\left(-y\right) + \left(-t\right)\right)\right)} \cdot x}{z} \]

      5. neg-mul-1 69.3%

         \[\leadsto \frac{\left(-\left(\color{blue}{-1 \cdot y} + \left(-t\right)\right)\right) \cdot x}{z} \]

      6. sub-neg 69.3%

         \[\leadsto \frac{\left(-\color{blue}{\left(-1 \cdot y - t\right)}\right) \cdot x}{z} \]

      7. distribute-lft-neg-in 69.3%

         \[\leadsto \frac{\color{blue}{-\left(-1 \cdot y - t\right) \cdot x}}{z} \]

      8. distribute-neg-frac 69.3%

         \[\leadsto \color{blue}{-\frac{\left(-1 \cdot y - t\right) \cdot x}{z}} \]

      9. associate-/l* 71.9%

         \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{\frac{z}{x}}} \]

      10. associate-/r/ 83.3%

          \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{z} \cdot x} \]

      11. distribute-lft-neg-in 83.3%

          \[\leadsto \color{blue}{\left(-\frac{-1 \cdot y - t}{z}\right) \cdot x} \]

   4. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{y + t}{z} \cdot x} \]

   5. Taylor expanded in y around 0 62.1%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-/l* 64.6%

         \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]

      2. associate-/r/ 73.8%

         \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   7. Simplified 73.8%

      \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   if -5.50000000000000035e142 < t < 9.4999999999999997e211

   1. Initial program 93.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in y around inf 77.1%

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
   3. Step-by-step derivation

      1. associate-*l/ 76.4%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]

   4. Simplified 76.4%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]

   if 9.4999999999999997e211 < t

   1. Initial program 99.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 59.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 69.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 69.0%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around 0 58.5%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+211}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 9: 67.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+210}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7e+142)
   (* x (/ t z))
   (if (<= t 4.4e+210) (/ x (/ z y)) (/ x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e+142) {
		tmp = x * (t / z);
	} else if (t <= 4.4e+210) {
		tmp = x / (z / y);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-7d+142)) then
        tmp = x * (t / z)
    else if (t <= 4.4d+210) then
        tmp = x / (z / y)
    else
        tmp = x / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e+142) {
		tmp = x * (t / z);
	} else if (t <= 4.4e+210) {
		tmp = x / (z / y);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7e+142:
		tmp = x * (t / z)
	elif t <= 4.4e+210:
		tmp = x / (z / y)
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7e+142)
		tmp = Float64(x * Float64(t / z));
	elseif (t <= 4.4e+210)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7e+142)
		tmp = x * (t / z);
	elseif (t <= 4.4e+210)
		tmp = x / (z / y);
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7e+142], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+210], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.99999999999999995e142

   1. Initial program 99.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 69.3%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. sub-neg 69.3%

         \[\leadsto \frac{\color{blue}{\left(y + \left(--1 \cdot t\right)\right)} \cdot x}{z} \]

      2. remove-double-neg 69.3%

         \[\leadsto \frac{\left(\color{blue}{\left(-\left(-y\right)\right)} + \left(--1 \cdot t\right)\right) \cdot x}{z} \]

      3. neg-mul-1 69.3%

         \[\leadsto \frac{\left(\left(-\left(-y\right)\right) + \left(-\color{blue}{\left(-t\right)}\right)\right) \cdot x}{z} \]

      4. distribute-neg-in 69.3%

         \[\leadsto \frac{\color{blue}{\left(-\left(\left(-y\right) + \left(-t\right)\right)\right)} \cdot x}{z} \]

      5. neg-mul-1 69.3%

         \[\leadsto \frac{\left(-\left(\color{blue}{-1 \cdot y} + \left(-t\right)\right)\right) \cdot x}{z} \]

      6. sub-neg 69.3%

         \[\leadsto \frac{\left(-\color{blue}{\left(-1 \cdot y - t\right)}\right) \cdot x}{z} \]

      7. distribute-lft-neg-in 69.3%

         \[\leadsto \frac{\color{blue}{-\left(-1 \cdot y - t\right) \cdot x}}{z} \]

      8. distribute-neg-frac 69.3%

         \[\leadsto \color{blue}{-\frac{\left(-1 \cdot y - t\right) \cdot x}{z}} \]

      9. associate-/l* 71.9%

         \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{\frac{z}{x}}} \]

      10. associate-/r/ 83.3%

          \[\leadsto -\color{blue}{\frac{-1 \cdot y - t}{z} \cdot x} \]

      11. distribute-lft-neg-in 83.3%

          \[\leadsto \color{blue}{\left(-\frac{-1 \cdot y - t}{z}\right) \cdot x} \]

   4. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{y + t}{z} \cdot x} \]

   5. Taylor expanded in y around 0 62.1%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   6. Step-by-step derivation

      1. associate-/l* 64.6%

         \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]

      2. associate-/r/ 73.8%

         \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   7. Simplified 73.8%

      \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

   if -6.99999999999999995e142 < t < 4.39999999999999974e210

   1. Initial program 93.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 80.6%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 80.6%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 79.1%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 79.1%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 79.1%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around inf 76.7%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{y}}} \]

   if 4.39999999999999974e210 < t

   1. Initial program 99.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
   3. Step-by-step derivation

      1. *-commutative 59.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

      2. associate-/l* 69.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

      3. neg-mul-1 69.0%

         \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

   5. Taylor expanded in y around 0 58.5%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+210}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 10: 61.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{x}{z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* y (/ x z)))

C

double code(double x, double y, double z, double t) {
	return y * (x / z);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = y * (x / z)
end function

Java

public static double code(double x, double y, double z, double t) {
	return y * (x / z);
}

Python

def code(x, y, z, t):
	return y * (x / z)

Julia

function code(x, y, z, t)
	return Float64(y * Float64(x / z))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = y * (x / z);
end

Wolfram

code[x_, y_, z_, t_] := N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.6%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

2. Taylor expanded in z around inf 77.2%

   \[\leadsto \color{blue}{\frac{\left(y - -1 \cdot t\right) \cdot x}{z}} \]
3. Step-by-step derivation

   1. *-commutative 77.2%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]

   2. associate-/l* 79.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]

   3. neg-mul-1 79.0%

      \[\leadsto \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

4. Simplified 79.0%

   \[\leadsto \color{blue}{\frac{x}{\frac{z}{y - \left(-t\right)}}} \]

5. Taylor expanded in y around inf 64.2%

   \[\leadsto \color{blue}{\frac{y \cdot x}{z}} \]
6. Step-by-step derivation

   1. associate-*r/ 63.4%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

7. Simplified 63.4%

   \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

8. Final simplification 63.4%

   \[\leadsto y \cdot \frac{x}{z} \]

Developer target: 94.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023171 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))